{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "98333d1d-9f2e-4330-af2d-f5fa83b89213",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b794f5f4-f8d0-4d35-8a9d-065a2c4b9475",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 生成正态分布的数据\n",
    "mean, std = -10, 4  # 均值和标准差\n",
    "x = np.linspace(-20, 20, 2000)\n",
    "y = np.exp(-(x - mean)**2 / (2 * std**2)) / (np.sqrt(2 * np.pi) * std)\n",
    "\n",
    "# 创建一个y轴的最小值，用于填充至该值\n",
    "y_min = np.min(y) * 0.1  # 可以根据需要调整这个值\n",
    "\n",
    "# 画图\n",
    "plt.plot(x, y, c='blue', label='IN')\n",
    "plt.ylim(0, 0.2)\n",
    "# 使用fill_between函数为曲线下面填色\n",
    "plt.fill_between(x, y_min, y, where=(y >= y_min), color='blue', alpha=0.5)\n",
    "\n",
    "# plt.title('IN')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Probability Density')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d61afb9a-30fe-4162-8797-8bfa3e2d92b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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sj2wJUmlpKTIzMxEbG3snGCcnxMbGIiMj44HOffr0aQQFBaF58+YYOXIkcnNzDY9lZmairKzM6HXDw8PRtGnTB35dIiIicgyyJUhXr16FTqdDQECA0fGAgACo1eoanzc6OhofffQRUlNTsXLlSpw7dw69e/fGjRs3AABqtRqurq7w9vY263VLSkqg1WqNNiIiInJM9eQOwNIGDhxo2O/QoQOio6PRrFkzfPrppxg7dmyNz5uUlIR58+ZZIkQiIiKycbL1IPn5+cHZ2bnC6LH8/Px7FmCby9vbG61bt8aZM2cAACqVCqWlpSgsLDTrdRMTE6HRaAzbhQsXLBYjERER2RbZEiRXV1dERUUhLS3NcEyv1yMtLQ0xMTEWe52bN2/i7NmzCAwMBABERUXBxcXF6HVzcnKQm5t7z9d1c3ODl5eX0UZERESOSdZbbAkJCYiPj0eXLl3QrVs3JCcno6ioCGPGjAEAjBo1CsHBwUhKSgIgCrtPnDhh2L906RKys7Ph6emJli1bAgCmT5+Ov/71r2jWrBkuX76MOXPmwNnZGSNGjAAAKJVKjB07FgkJCfD19YWXlxcmT56MmJgYdO/eXYZ/BSIiIrI1siZIw4YNw5UrVzB79myo1WpERkYiNTXVULidm5sLJ6c7nVyXL19Gp06dDN8vXrwYixcvRt++fZGeng4AuHjxIkaMGIFr166hcePG6NWrF/bv34/GjRsbnrdkyRI4OTlh6NChKCkpQVxcHD744IPauWgiIiKyeQpJkiS5g7BHWq0WSqUSGo2Gt9uIiIjsRHU/v2VfaoSIiIjI1jBBIiIiIjLBBImIiIjIBBMkIiIiIhNMkIiIiIhMMEEiIiIiMsEEiYiIiMgEEyQiIiIiE0yQiIiIiEwwQSIiIiIywQSJiIiIyAQTJCIiIiITTJCIiIiITDBBIiIiIjLBBImIiIjIBBMkIiIiIhNMkIiIiIhMMEEiIiIiMsEEiYiIiMgEEyQiIiIiE0yQiIiIiEwwQSIiIiIyYXaCtHbtWhQXF1sjFiIiIiKbYHaCNHPmTKhUKowdOxb79u2zRkxEREREsjI7Qbp06RLWrVuHq1evol+/fggPD8e7774LtVptjfiIiIiIap3ZCVK9evXw1FNP4YsvvsCFCxcwbtw4rF+/Hk2bNsUTTzyBL774Anq93hqxEhEREdWKByrSDggIQK9evRATEwMnJyccPXoU8fHxaNGiBdLT0y0UIhEREVHtqlGClJ+fj8WLF+Ohhx5Cv379oNVqsW3bNpw7dw6XLl3C3//+d8THx1s6ViIiIqJaoZAkSTLnCX/961/x7bffonXr1vi///s/jBo1Cr6+vkZtCgoKoFKpHPpWm1arhVKphEajgZeXl9zhEBERUTVU9/O7nrkn9vf3x+7duxETE1Nlm8aNG+PcuXPmnpqIiIjIJph9i61v377o3LlzheOlpaX4+OOPAQAKhQLNmjV78OiIiIiIZGD2LTZnZ2fk5eXB39/f6Pi1a9fg7+8PnU5n0QBtFW+xERER2Z/qfn6b3YMkSRIUCkWF4xcvXoRSqTT3dEREREQ2p9o1SJ06dYJCoYBCoUD//v1Rr96dp+p0Opw7dw4DBgywSpBEREREtanaCdLgwYMBANnZ2YiLi4Onp6fhMVdXV4SGhmLo0KEWD5CIiIiotlU7QZozZw4AIDQ0FMOGDYO7u7vVgiIiIiKSk9k1SPHx8RZNjlasWIHQ0FC4u7sjOjoaBw8erLLt8ePHMXToUISGhkKhUCA5OblCm6SkJHTt2hUNGzaEv78/Bg8ejJycHKM2/fr1M9wuLN9eeOEFi10TERER2bdqJUi+vr64evUqAMDHxwe+vr5VbubYvHkzEhISMGfOHGRlZaFjx46Ii4tDQUFBpe2Li4vRvHlzLFiwACqVqtI2u3fvxsSJE7F//37s2LEDZWVleOyxx1BUVGTUbty4ccjLyzNsCxcuNCt2IiIiclzVusW2ZMkSNGzY0LBf2Si2mnj//fcxbtw4jBkzBgCQkpKCr7/+GmvWrMHMmTMrtO/atSu6du0KAJU+DgCpqalG33/00Ufw9/dHZmYm+vTpYzju4eFRZZJFREREdVu1EqS711UbPXq0RV64tLQUmZmZSExMNBxzcnJCbGwsMjIyLPIaAKDRaACgQu/W+vXr8cknn0ClUuGvf/0r3njjDXh4eFR5npKSEpSUlBi+12q1FouRiIiIbIvZNUhZWVk4evSo4fsvvvgCgwcPxmuvvYbS0tJqn+fq1avQ6XQICAgwOh4QEAC1Wm1uWJXS6/WYOnUqevbsifbt2xuOP/PMM/jkk0+wa9cuJCYm4j//+Q+effbZe54rKSkJSqXSsIWEhFgkRiIiIrI9ZidI//jHP/DLL78AAH799VcMGzYMHh4e2LJlC2bMmGHxAB/ExIkTcezYMWzatMno+Pjx4xEXF4eIiAiMHDkSH3/8MT7//HOcPXu2ynMlJiZCo9EYtgsXLlg7fCIiIpKJ2QnSL7/8gsjISADAli1b0LdvX2zYsAEfffQR/vvf/1b7PH5+fnB2dkZ+fr7R8fz8fIvUBk2aNAnbtm3Drl270KRJk3u2jY6OBgCcOXOmyjZubm7w8vIy2oiIiMgx1WipEb1eDwDYuXMnBg0aBAAICQkxjHSrDldXV0RFRSEtLc1wTK/XIy0tDTExMeaGZRTfpEmT8Pnnn+P7779HWFjYfZ+TnZ0NAAgMDKzx6xIREZHjqPZEkeW6dOmCt956C7Gxsdi9ezdWrlwJADh37lyFeqL7SUhIQHx8PLp06YJu3bohOTkZRUVFhlFto0aNQnBwMJKSkgCIwu4TJ04Y9i9duoTs7Gx4enqiZcuWAMRttQ0bNuCLL75Aw4YNDfVMSqUS9evXx9mzZ7FhwwYMGjQIjRo1wpEjRzBt2jT06dMHHTp0MPefg4iIiByRZKaff/5Zat++veTl5SXNnTvXcHzSpEnSiBEjzD2dtGzZMqlp06aSq6ur1K1bN2n//v2Gx/r27SvFx8cbvj937pwEoMLWt29fQ5vKHgcgrV27VpIkScrNzZX69Okj+fr6Sm5ublLLli2lV155RdJoNGbFrdFoJABmP4+IiIjkU93Pb4UkSZIlEq1bt27B2dkZLi4uljidzdNqtVAqldBoNKxHIiIishPV/fw2+xZbudLSUhQUFBjqkco1bdq0pqckIiIisglmJ0i//PILxo4di3379hkdlyQJCoUCOp3OYsERERERycHsBGnMmDGoV68etm3bhsDAQIstO0JERERkK8xOkLKzs5GZmYnw8HBrxENEREQkO7PnQWrXrp1Z8x0RERER2RuzE6R3330XM2bMQHp6Oq5duwatVmu0EREREdk7s4f5OzmJnMq09qiuFWlzmD8REZH9sdow/127dj1QYERERES2zuwEqW/fvtaIg4iIiMhmmF2DBAA//PADnn32WfTo0QOXLl0CAPznP//B3r17LRocERERkRzMTpD++9//Ii4uDvXr10dWVhZKSkoAABqNBu+8847FAyQiIiKqbWYnSG+99RZSUlKwatUqo3XXevbsiaysLIsGR0RERCQHsxOknJwc9OnTp8JxpVKJwsJCS8REREREJCuzEySVSoUzZ85UOL537140b97cIkERERERycnsBGncuHGYMmUKDhw4AIVCgcuXL2P9+vWYPn06JkyYYI0YiYiIiGqV2cP8Z86cCb1ej/79+6O4uBh9+vSBm5sbpk+fjsmTJ1sjRiIiIqJaZfZM2uVKS0tx5swZ3Lx5E+3atYOnp6elY7NpnEmbiIjI/lhtJm1ALCui1WoREBCAdu3a1ThIIiIiIltkVg2SWq3GqFGj4OPjg4CAAPj7+8PHxwfPP/888vPzrRUjERERUa2qdg+SVqtFjx49cPPmTYwZMwbh4eGQJAknTpzAxo0bsXfvXmRlZdW5W21ERETkeKqdIP3zn/+Es7Mzjh8/jsaNGxs9NmvWLPTs2RNLly7Fa6+9ZvEgiYiIiGpTtW+xff3113jttdcqJEcA4O/vj8TERHz11VcWDY6IiIhIDtVOkH755Rf06NGjysd79OiBnJwciwRFREREJKdqJ0harRbe3t5VPu7t7Q2tVmuJmIiIiIhkVe0ESZIkODlV3VyhUKCGUyoRERER2ZRqF2lLkoTWrVtDoVBU+TgRERGRI6h2grR27VprxkFERERkM6qdIMXHx1szDiIiIiKbYdZM2kRERER1ARMkIiIiIhNMkIiIiIhMMEEiIiIiMmF2grRr1y5rxEFERERkM8xOkAYMGIAWLVrgrbfewoULF6wRExEREZGszE6QLl26hEmTJuGzzz5D8+bNERcXh08//RSlpaXWiI+IiIio1pmdIPn5+WHatGnIzs7GgQMH0Lp1a7z44osICgrCSy+9hJ9//tms861YsQKhoaFwd3dHdHQ0Dh48WGXb48ePY+jQoQgNDYVCoUBycnKNznnr1i1MnDgRjRo1gqenJ4YOHYr8/Hyz4iYiIiLH9UBF2p07d0ZiYiImTZqEmzdvYs2aNYiKikLv3r1x/Pjx+z5/8+bNSEhIwJw5c5CVlYWOHTsiLi4OBQUFlbYvLi5G8+bNsWDBAqhUqhqfc9q0afjqq6+wZcsW7N69G5cvX8aQIUNq9o9AREREjkeqgdLSUmnLli3SwIEDpXr16kndu3eXVq1aJd28eVM6d+6cNHLkSKlt27b3PU+3bt2kiRMnGr7X6XRSUFCQlJSUdN/nNmvWTFqyZInZ5ywsLJRcXFykLVu2GNqcPHlSAiBlZGTc93XLaTQaCYCk0Wiq/RwiIiKSV3U/v6u91Ei5yZMnY+PGjZAkCc899xwWLlyI9u3bGx5v0KABFi9ejKCgoHuep7S0FJmZmUhMTDQcc3JyQmxsLDIyMswNq9rnzMzMRFlZGWJjYw1twsPD0bRpU2RkZKB79+6VnrukpAQlJSWG77VabY1iJCIiKygrA/bvBw4dAs6dA27dAtzcgBYtgKgoICYGcHGRO0qyI2YnSCdOnMCyZcswZMgQuLm5VdrGz8/vvtMBXL16FTqdDgEBAUbHAwICcOrUKXPDqvY51Wo1XF1d4e3tXaGNWq2u8txJSUmYN29ejeIiIiIrOXMGWLYM+PhjoLCw6nZeXsBzzwFTpgCtWtVaeGS/zK5BmjNnDp5++ukKydHt27exZ88eAEC9evXQt29fy0RoIxITE6HRaAwbpzggIpLR778D06YBbdsCS5eK5MjNDQgKAlq3BiIixGPBwYCrK6DVAitWAOHhwAsvANevy30FZOPM7kF6+OGHkZeXB39/f6PjGo0GDz/8MHQ6XbXO4+fnB2dn5wqjx/Lz86sswLbEOVUqFUpLS1FYWGjUi3S/13Vzc6uyx4yIiGpRejrw7LPApUvi+4AAkQxFRoqeIoXCuL1OB5w8CWRkAJcvA//6F/D558DGjcAjj9R29GQnzO5BkiQJCtMfPgDXrl1DgwYNqn0eV1dXREVFIS0tzXBMr9cjLS0NMTEx5oZV7XNGRUXBxcXFqE1OTg5yc3Nr/LpERFQLJAlYuFAkNZcuAQ0bAn36AGPGAH37AkplxeQIAJydgfbtgXHjgOHDxfMKCoDYWODNN8V5iUxUuwepfBi8QqHA6NGjjXpTdDodjhw5gh49epj14gkJCYiPj0eXLl3QrVs3JCcno6ioCGPGjAEAjBo1CsHBwUhKSgIgirBPnDhh2L906RKys7Ph6emJli1bVuucSqUSY8eORUJCAnx9feHl5YXJkycjJiamygJtIiKSmU4HTJ4MrFwpvm/WDBgwADD3jkObNkBYGPDFF8CJE8Ds2aKOac0akUgR/anaCZJSqQQgepAaNmyI+vXrGx5zdXVF9+7dMW7cOLNefNiwYbhy5Qpmz54NtVqNyMhIpKamGoqsc3Nz4eR0p5Pr8uXL6NSpk+H7xYsXY/Hixejbty/S09OrdU4AWLJkCZycnDB06FCUlJQgLi4OH3zwgVmxExFRLdHrgeefF4XYgKgvGjQIcHev2flcXYGnnwb27gXS0sR5i4uBzZsBJ67hToJCkszrW5w3bx6mT59u1u00R6TVaqFUKqHRaODl5SV3OEREjkmSgBdfBFJSxO2zrl2BRx8F6pldQlu5o0dFPZIkASNGAJ98wiTJwVX387tGo9jqenJERES1ZN48kRwBQJcuwGOPWS45AkRv1ODBYn/jRuCVVyx3brJr1fop69y5M9LS0uDj44NOnTpVWqRdLisry2LBERFRHbZli0iQADFC7bHHrFMn1KEDUFoKfP018P77wEMPiVt6VKdVK0F68sknDUXZg8szbSIiIms5fBiIjxf7LVqIgmxL9hyZ6tIFuHoVOHAA+Mc/RJIUHW291yObZ3YNEgmsQSIishKtFujUCfj1VzHH0YgRYgi/ten1wPr14nVVKuDUqdp5XapVVqtBIiIisqqJE0WS0qABMHBg7SUpTk7A3/4GeHoCarWYM4l9CHVWtforfXx87ll3dLfrnL6diIhq6j//ESPJFAqxwGyzZrX7+vXrA3//O7B2LZCaCixfLuZfojqnWglScnKylcMgIqI67+JF0XsEiAkd5Zq8NyQE6NcP2LULmDEDeOKJ2k/USHbVSpDiywvliIiIrKF8vqMbN4BGjYC4OHlntu7VS9Qg5eWJW2379lW+jAk5rGrVIGm1WqP9e21ERERm+/RT4KuvRB1Qjx7AXYuJy8LJCXjqKfF1/36Aqy3UOdUaxebs7Iy8vDz4+/vDycmp0nqk8kVsdTqdVQK1NRzFRkRkIdeuAW3bAleuAOHhYhkQW5nNes8ecautQQPg/HnAz0/uiOgBVffzu1q32L7//nv4+voCAHbt2mWZCImIiADg9ddFcqRUArGxtpMcAUDPnsCRIyKJe+EF4LPP5I6IagnnQaoh9iAREVlAdjbQubOoQXrkEaB3b7kjquj8eWDdOrG/d69ImshuWbQHydTvv/+O1atX4+TJkwCAdu3aYcyYMYZeJiIiovuSJGDKFPG1SRPbnbk6NBRo1w44cQIYO1Z8taVeLrIKs9/hPXv2IDQ0FEuXLsXvv/+O33//HUuXLkVYWBj27NljjRiJiMgRbdkianzq1RO9Mq6uckdUtbg4EWdODrBihdzRUC0w+xZbREQEYmJisHLlSjj/OQRTp9PhxRdfxL59+3D06FGrBGpreIuNiOgB/PGHKMjOzbW9wuyq/PAD8P33gK+vmLOpfn25I6IasNpSI2fOnMHLL79sSI4AMcotISEBZ86cqVm0RERUt6xYIZKjBg2Avn1tPzkCxMSVDRoA168Dc+fKHQ1Zmdk/kZ07dzbUHt3t5MmT6Nixo0WCIiIiB6bRAElJYj88XCxIaw9cXEQhOQAsWyZGtpHDqlaR9pEjRwz7L730EqZMmYIzZ86g+5/TwO/fvx8rVqzAggULrBMlERE5jsWLRS+Ml5cYtWZPM1RHRopZta9dAxIS7oxuI4dTrRqk8skh79eUE0USEdE95ecDLVoARUVixuxHH5U7IvP98guwcaMo2j59WoxyI7th0WH+586ds1hgRERUh73zjkiOfH1FgmSPWrUCgoOBS5eAV14Ro/HI4VQrQWrGVYyJiOhBXbgApKSI/Q4dRMGzPVIoRC3Sf/4DfP45cO4cEBYmd1RkYTWaKBIATpw4gdzcXJSWlhodf+KJJx44KCIickCLFgGlpUDjxkC3bnJH82DCwsTklhcvAjNmsBfJAZmdIP3666946qmncPToUaO6pPIFbOtKDRIREZlBrQZWrRL77dvb/xxC5b1IH3/MXiQHZfYw/ylTpiAsLAwFBQXw8PDA8ePHsWfPHnTp0gXp6elWCJGIiOzee+8Bt24BjRoBXbvKHY1lhIaKXiSdTtQikUMxO0HKyMjA/Pnz4efnBycnJzg5OaFXr15ISkrCSy+9ZI0YiYjInl29CqxcKfYfesj+e4/KlfciAcDWrWLiS3IYZidIOp0ODRs2BAD4+fnh8uXLAEQhd05OjmWjIyIi+5ecLEau+fjY7oK0NRUaKka06XTArFlyR0MWZHaC1L59e/z8888AgOjoaCxcuBA//vgj5s+fj+bNm1s8QCIismOFhWLWaQBo1w7w8JA1HItTKMRklwDw6adiAkxyCGYnSLNmzYJerwcAzJ8/H+fOnUPv3r2xfft2LF261OIBEhGRHVuxAtBqAaXS8XqPyrVuLWqrSkqAefPkjoYspFozad/P9evX4ePjYxjJVhdwJm0iovu4dUvcgsrPF8P6Bw6UOyLryc4GvvgCaNhQXK+j1Fk5oOp+fj/Q8skXLlzAhQsX4OvrW6eSIyIiqob160Wy4OHhuL1H5SIiRHJ044aY74nsntkJ0u3bt/HGG29AqVQiNDQUoaGhUCqVmDVrFsrKyqwRIxER2Ru9XgztB8Taaz4+8sZjbc7Od5ZOWb5cFG2TXTM7QZo8eTI+/PBDLFy4EIcPH8bhw4excOFCrF69msP8iYhISE0FTp4EXFxE71FduMvQuTPg5gZcuXJnUkyyW2bXICmVSmzatAkDTe4lb9++HSNGjIBGo7FogLaKNUhERPfwyCPArl1Ay5bAM8/UjQQJAL7/HvjhB1G4zalvbJLVapDc3NwQGhpa4XhYWBhcXV3NPR0RETmazEyRHDk5AV261J3kCBCzhDs5Ab/8AuzcKXc09ADMTpAmTZqEN998EyUlJYZjJSUlePvttzFp0iSLBkdERHaovPYoOFj0INUlDRuK2cIB4O235Y2FHki1EqQhQ4YYtuzsbGzbtg1NmjRBbGwsYmNj0aRJE3z11VeGCSTNtWLFCoSGhsLd3R3R0dE4ePDgPdtv2bIF4eHhcHd3R0REBLZv3270uEKhqHRbdNfIgtDQ0AqPL1iwoEbxExHRn3JzxYSJANChgyhermu6dxdf9+wBzp6VNxaqsXrVaaRUKo2+Hzp0qNH3ISEhNQ5g8+bNSEhIQEpKCqKjo5GcnIy4uDjk5OTA39+/Qvt9+/ZhxIgRSEpKwl/+8hds2LABgwcPRlZWFtq3bw8AyMvLM3rON998g7Fjx1aIe/78+Rg3bpzh+/IlVIiIqIZSUsQIrsaNxdD3uigoCAgJAS5cAObPB9atkzsiqgGLTBT5IKKjo9G1a1csX74cAKDX6xESEoLJkydj5syZFdoPGzYMRUVF2LZtm+FY9+7dERkZiZSUlEpfY/Dgwbhx4wbS0tIMx0JDQzF16lRMnTq1RnGzSJuIyERpqUgMCgrEkPdHH5U7IvmcPCl60jw8xFxQnp5yR0R/svpEkVeuXMHevXuxd+9eXLlypUbnKC0tRWZmJmJjY+8E5OSE2NhYZGRkVPqcjIwMo/YAEBcXV2X7/Px8fP311xg7dmyFxxYsWIBGjRqhU6dOWLRoEW7fvl1lrCUlJdBqtUYbERHd5X//E8lR/fqiWLkua9MG8PICiovv1GSRXTE7QSoqKsLzzz+PwMBA9OnTB3369EFQUBDGjh2L4uJis8519epV6HQ6BAQEGB0PCAiAWq2u9Dlqtdqs9uvWrUPDhg0xZMgQo+MvvfQSNm3ahF27duEf//gH3nnnHcyYMaPKWJOSkqBUKg3bg9xWJCJySB98IL42awZ4e8saiuycnO7UIv3rX4C8N2uoBsxOkBISErB792589dVXKCwsRGFhIb744gvs3r0bL7/8sjVifCBr1qzByJEj4e7ubnQ8ISEB/fr1Q4cOHfDCCy/gvffew7Jly4xG590tMTERGo3GsF24cKE2wicisg/Hjon5fxQK9h6V69RJTJSZlwds3ix3NGQmsxOk//73v1i9ejUGDhwILy8veHl5YdCgQVi1ahU+++wzs87l5+cHZ2dn5OfnGx3Pz8+HSqWq9Dkqlara7X/44Qfk5OTg//7v/+4bS3R0NG7fvo3z589X+ribm5vhess3IiL6U3kNqEolFqglwN0diIwU+++/L2soZD6zE6Ti4uIKt7gAwN/f3+xbbK6uroiKijIqntbr9UhLS0NMTEylz4mJiTFqDwA7duyotP3q1asRFRWFjh073jeW7OxsODk5VTpyjoiI7uHmTeDjj8V+RIS4vURCt27i66FDonCb7IbZP8UxMTGYM2cObt26ZTj2xx9/YN68eVUmNfeSkJCAVatWYd26dTh58iQmTJiAoqIijBkzBgAwatQoJCYmGtpPmTIFqampeO+993Dq1CnMnTsXP/30U4VJKrVaLbZs2VJp71FGRgaSk5Px888/49dff8X69esxbdo0PPvss/Bx9AUViYgsbf16sYq9p6dYj4zu8PO706P2zjuyhkLmqdY8SHdLTk7GgAED0KRJE0PPzM8//wx3d3d8++23ZgcwbNgwXLlyBbNnz4ZarUZkZCRSU1MNvVS5ublwuuuvkR49emDDhg2YNWsWXnvtNbRq1Qpbt241zIFUbtOmTZAkCSNGjKjwmm5ubti0aRPmzp2LkpIShIWFYdq0aUhISDA7fiKiOk2SgJUrxX6LFmKxVjLWrRtw/rwY5ffhh2KUH9m8Gs2DVFxcjPXr1+PUqVMAgLZt22LkyJGoX4fedM6DREQEICNDzHnk7AyMHw+wTKEivR5YskTcily4EHjlFbkjqtOq+/ltVg9SWVkZwsPDsW3bNqMZqImIqI4qH9rfpImYPZsqKl+0Nz1dDPlngmQXzKpBcnFxMao9IiKiOuzq1TvrrnXqJIb4U+WiokSidPasSJTI5pldpD1x4kS8++6795x1moiI6oC1a8XyIt7egEkdKJnw9ATCw8X+u+/KGwtVi9lF2ocOHUJaWhq+++47REREoEGDBkaP/+9//7NYcEREZKP0+jtzH4WHixokurdu3YATJ4CdO8WSLKzXsmlmJ0je3t4YOnSoNWIhIiJ78d13wK+/ipmiy5fUoHtr2lTUaV25AixaJDayWTUaxUYcxUZEddyTTwJffgm0bAmMHCl3NPbjp5+Ar78WiZJazUk1ZVDdz+9qvzN6vR7vvvsuevbsia5du2LmzJn4448/LBIsERHZkdxcYNs2sc9118zToYPodbty5U6BO9mkaidIb7/9Nl577TV4enoiODgY//znPzFx4kRrxkZERLboww9FDVLjxkCrVnJHY19cXe+sz7Zkiayh0L1VO0H6+OOP8cEHH+Dbb7/F1q1b8dVXX2H9+vXQ6/XWjI+IiGxJaSnw73+L/XbtOLS/Jsp73Q4dAk6fljcWqlK1E6Tc3FwMGjTI8H1sbCwUCgUuX75slcCIiMgGff45kJ8vVqovX4iVzNO4MRASIpZpWbBA7mioCtVOkG7fvg13d3ejYy4uLigrK7N4UEREZKPK111r3hzw8JA3FntWnlx+9pnolSObU+1h/pIkYfTo0XC7ayHCW7du4YUXXjCaC4nzIBEROagTJ4Ddu8VttehouaOxb23bigRTqwVWrwYmTJA7IjJR7QQpPj6+wrFnn33WosEQEZENK+89UqnELSKqOWdnoHNnYO9esZ4dEySbU+0Eae3atdaMg4iIbNnNm8DHH4v9iAgWZ1tCly7Ajz8Cx44Bhw+L9ezIZnCGKiIiur+NG8XtIE9P0fNBD06pBFq0EPtJSfLGQhUwQSIionuTJHEbCBAf6HfVotIDKi/W3rYNKCqSNxYywgSJiIju7cABIDtb1M1w3TXLatkS8PIC/vgDWL5c7mjoLkyQiIjo3sqLs4ODgYAAeWNxNArFnYkjP/xQ3ljICBMkIiKq2rVrwObNYr9jRxZnW0OnTmLR2l9/FdMokE1ggkRERFVbuxYoKQG8vYH27eWOxjE1aCDmRQKAhQvljYUMmCAREVHl9HogJUXst2wpFlol6ygv1t6xA7h+Xd5YCAATJCIiqsqOHcDZs4CLC2fOtraQEMDPDygrA957T+5oCEyQiIioKuXF2U2bAo0ayRuLo1Mo7vQirV0rplYgWTFBIiKiii5cAL76SuxHRrI4uzZ06CB66/LyxLxIJCsmSEREVNGHH4oapMaNgfBwuaOpG9zcxDIuALB4sbyxEBMkIiIyUVYG/PvfYr9VK6BetZftpAdVfptt717g4kV5Y6njmCAREZGxrVsBtRpwdxcLqlLtCQgAgoJE7x2H/MuKCRIRERkrX3etWTMx/xHVrvIRg598Aty+LW8sdRgTJCIiuuPkSSA9XRRld+7M4mw5tGsneu9+/x3YtEnuaOosJkhERHRH+cSQKhXQvLm8sdRV9eqJ5BQAkpNlDaUuY4JERERCURGwbp3Yb9OGxdlyKq/9yswETp2SN5Y6igkSEREJGzcCGg3g6XmnB4Pk4eMDhIWJ/XfflTeWOooJEhERiZmby2fODgsDGjaUNx66U6y9ZQvwxx/yxlIHMUEiIiLg4EEgKwtwdmbvka1o1Ur05hUVieVHqFYxQSIiImDFCvE1OFgsnEryc3ICunYV+8uWyRtLHWQTCdKKFSsQGhoKd3d3REdH4+DBg/dsv2XLFoSHh8Pd3R0RERHYvn270eOjR4+GQqEw2gYMGGDU5vr16xg5ciS8vLzg7e2NsWPH4ubNmxa/NiIim3f1KrB5s9hv1070IpFt6NxZJEqnTolePqo1sidImzdvRkJCAubMmYOsrCx07NgRcXFxKCgoqLT9vn37MGLECIwdOxaHDx/G4MGDMXjwYBw7dsyo3YABA5CXl2fYNm7caPT4yJEjcfz4cezYsQPbtm3Dnj17MH78eKtdJxGRzVq9GigtBXx976wFRrbB0xNo3Vrss1i7VikkSZLkDCA6Ohpdu3bF8uXLAQB6vR4hISGYPHkyZs6cWaH9sGHDUFRUhG13rXTcvXt3REZGIuXP+TtGjx6NwsJCbN26tdLXPHnyJNq1a4dDhw6hy59DKVNTUzFo0CBcvHgRQUFB941bq9VCqVRCo9HAy8vL3MsmIrINOh3QogXw229AVBTwl7/IHRGZOn9eTL/g6goUFABKpdwR2bXqfn7L2oNUWlqKzMxMxMbGGo45OTkhNjYWGRkZlT4nIyPDqD0AxMXFVWifnp4Of39/tGnTBhMmTMC1a9eMzuHt7W1IjgAgNjYWTk5OOHDgQKWvW1JSAq1Wa7QREdm9b74RyZGbm0iQyPY0ayaG/ZeWAn92JpD1yZogXb16FTqdDgEBAUbHAwICoFarK32OWq2+b/sBAwbg448/RlpaGt59913s3r0bAwcOhE6nM5zD39/f6Bz16tWDr69vla+blJQEpVJp2EJYxEhEjqC8ODskRMyeTbZHobgz5D8lRUzJQFYnew2SNQwfPhxPPPEEIiIiMHjwYGzbtg2HDh1Cenp6jc+ZmJgIjUZj2C5cuGC5gImI5HDmDJCaKvY7dOC6a7asY0cxs/nFi8COHXJHUyfImiD5+fnB2dkZ+fn5Rsfz8/OhquIvGZVKZVZ7AGjevDn8/Pxw5swZwzlMi8Bv376N69evV3keNzc3eHl5GW1ERHbt7nXX2rSRNxa6N3d3oH17sb9wobyx1BGyJkiurq6IiopCWlqa4Zher0daWhpiYmIqfU5MTIxRewDYsWNHle0B4OLFi7h27RoCAwMN5ygsLERmZqahzffffw+9Xo/o8m5MIiJHVlwMrFkj9lu2FAXAZNu6dRNf09OBKspByHJkv8WWkJCAVatWYd26dTh58iQmTJiAoqIijBkzBgAwatQoJCYmGtpPmTIFqampeO+993Dq1CnMnTsXP/30EyZNmgQAuHnzJl555RXs378f58+fR1paGp588km0bNkScXFxAIC2bdtiwIABGDduHA4ePIgff/wRkyZNwvDhw6s1go2IyO5t2gT8/jvXXbMngYGit0+nYy9SLZA9QRo2bBgWL16M2bNnIzIyEtnZ2UhNTTUUYufm5iIvL8/QvkePHtiwYQM+/PBDdOzYEZ999hm2bt2K9n92PTo7O+PIkSN44okn0Lp1a4wdOxZRUVH44Ycf4ObmZjjP+vXrER4ejv79+2PQoEHo1asXPvzww9q9eCIiOUjSneLsZs0Ab29ZwyEzlN/l+PhjkSiR1cg+D5K94jxIRGS3DhwAuncXM2aPHHln1XiyfbdvA4sXAyUlwPr1wDPPyB2R3bGLeZCIiEgG5et6BQcDTZvKGwuZp149oFMnsZ+cLGsojo4JEhFRXXL5MvDpp2L/oYe47po9Kp/k+NAhICdH3lgcGBMkIqK6ZOVKoKwMaNxYzH1E9qdRIyA0VOy/846soTgyJkhERHXFH3/cmfuoZUsxtw7Zp/Ih///9L3DrlryxOCgmSEREdcWGDcDVq0CDBlx3zd61aSOmaCgqApYulTsah8QEiYioLpAk4J//FPthYYCvr7zx0INxcrrTi7R8OddnswImSEREdcGuXcDRo2IUVFQU111zBF26iPfzwgVg61a5o3E4TJCIiOqC8iHhTZsCISGyhkIWUr8+EBkp9lmsbXFMkIiIHN3p08C2bWK/QwcO7Xck5euQ/vQTcPiwvLE4GCZIRESObtkyUaOiUgFt28odDVmSry/QurXYnztX1lAcDRMkIiJHVlgIrF0r9tu0AVxdZQ2HrKBHD/F1+3ZArZY3FgfCBImIyJGlpAA3bwJKJYf2O6qmTYGAALFO25tvyh2Nw2CCRETkqG7dujO0v1UroGFDeeMh61AogJ49xf7HH4sJQemBMUEiInJU//mPuOXSoMGdOXPIMbVrJyaOvHnzzmLE9ECYIBEROSKdDli8WOw3bw74+ckbD1mXszPQvbvYT04G9HpZw3EETJCIiBzRl18Cv/wCuLkBXbtyYsi6ICpKFOHn5QHr1skdjd1jgkRE5GgkCXj3XbHfrBkQHCxvPFQ73N1FMgyIiSO5/MgDYYJERORo9u4FDhwQt126dBHrdlHdEBMj3vczZ0QvItUYf2uIiBxNee9RSIioP6K6o0EDoFMnsc+JIx8IEyQiIkdy5Ajw9ddiv1MnLitSF/XsKWrOsrOB3bvljsZuMUEiInIkb70lvjZpwmVF6ipvb6B9e7H/+uuyhmLPmCARETmK48eBzz4T+x07Ai4u8sZD8undW3z98UcuYltDTJCIiBzF22+LkUvBwUBEhNzRkJwaN76ziO3MmfLGYqeYIBEROYKcHGDzZrHfoYOY/4jqtj59xNcdO0TvIpmFCRIRkSN45x0xe3JgoLi9RhQcDLRoIXoVX35Z7mjsDhMkIiJ7d+YMsH692I+IYO8R3fHII+Lrd9+JEY5UbUyQiIjs3TvviLXXVKo7c+AQAUBQENCypehFSkiQOxq7wgSJiMie5eTcWXcrIkIsN0F0t/JepLQ0jmgzAxMkIiJ7Nnv2ndqjqCi5oyFbFBh4Z0Qbe5GqjQkSEZG9ysoCPv1U7EdGsvaIqlbei5SeLtbpo/tigkREZK9mzRJfQ0JEgkRUlYCAOzOrT5kibyx2ggkSEZE9+uEH4JtvxJpbnTsDrq5yR0S2rn9/8fNy4ACwfbvc0dg8JkhERPZGku6ssdWs2Z11t4jupVEjkUwDwNSp4ueIqsQEiYjI3nz5pehBcnYGunUD6tWTOyKyF/36iZ+X06eB1avljsamMUEiIrInpaXAK6+I/RYtgDZt5I2H7IunJ9Czp9h//XXx80SVsokEacWKFQgNDYW7uzuio6Nx8ODBe7bfsmULwsPD4e7ujoiICGy/615qWVkZXn31VURERKBBgwYICgrCqFGjcPnyZaNzhIaGQqFQGG0LFiywyvUREVnMypXir393d/FB52QT/42TPenRA6hfHygoAJKS5I7GZsn+m7V582YkJCRgzpw5yMrKQseOHREXF4eCgoJK2+/btw8jRozA2LFjcfjwYQwePBiDBw/GsWPHAADFxcXIysrCG2+8gaysLPzvf/9DTk4OnnjiiQrnmj9/PvLy8gzb5MmTrXqtREQP5Pp1YN48sR8eLkavEZnL1fXOsP/Fi8XPFVWgkCR5q7Sio6PRtWtXLF++HACg1+sREhKCyZMnY+bMmRXaDxs2DEVFRdi2bZvhWPfu3REZGYmUlJRKX+PQoUPo1q0bfvvtNzRt2hSA6EGaOnUqpk6dWqO4tVotlEolNBoNvLy8anQOIiKzTJ0K/POfgLc38NxzgK+v3BGRvdLrgRUrRHL0zDN31vKrA6r7+S1rD1JpaSkyMzMRGxtrOObk5ITY2FhkZGRU+pyMjAyj9gAQFxdXZXsA0Gg0UCgU8Pb2Njq+YMECNGrUCJ06dcKiRYtw+/btml8MEZE1/fKL+EADgA4dmBzRg3FyAh5/XOxv2sQlSCoh69CHq1evQqfTISAgwOh4QEAATp06Velz1Gp1pe3VanWl7W/duoVXX30VI0aMMMoUX3rpJXTu3Bm+vr7Yt28fEhMTkZeXh/fff7/S85SUlKCkpMTwvVarrdY1EhE9MEkCXnoJuH1bLEjbvbvcEZEjaN5cLEHyyy/A88+LmdkVCrmjshkOPTa0rKwMf//73yFJElauXGn0WMJd69F06NABrq6u+Mc//oGkpCS4VTJdf1JSEuaV3/snIqpN//sf8O23Ylh/dLQosCWyhIEDgbNngexs4KOPgDFj5I7IZsh6i83Pzw/Ozs7Iz883Op6fnw+VSlXpc1QqVbXalydHv/32G3bs2HHfOqHo6Gjcvn0b58+fr/TxxMREaDQaw3bhwoX7XB0RkQXcvHlnaYiWLYGICHnjIcfi7S1GtQHA9OlAcbGs4dgSWRMkV1dXREVFIS0tzXBMr9cjLS0NMTExlT4nJibGqD0A7Nixw6h9eXJ0+vRp7Ny5E40aNbpvLNnZ2XBycoK/v3+lj7u5ucHLy8toIyKyuvnzgUuXxPw1ffuKXiQiS+rdG2jYUBRsc502A9lvsSUkJCA+Ph5dunRBt27dkJycjKKiIoz5s5tv1KhRCA4ORtKfczVMmTIFffv2xXvvvYfHH38cmzZtwk8//YQPP/wQgEiO/va3vyErKwvbtm2DTqcz1Cf5+vrC1dUVGRkZOHDgAB5++GE0bNgQGRkZmDZtGp599ln4+PjI8w9BRGTq2DFgyRKx37GjqD8isjQXF2DQIGDzZmDNGmD8eKBrV7mjkp3sCdKwYcNw5coVzJ49G2q1GpGRkUhNTTUUYufm5sLpronQevTogQ0bNmDWrFl47bXX0KpVK2zduhXt/1yL6NKlS/jyyy8BAJEmq1vv2rUL/fr1g5ubGzZt2oS5c+eipKQEYWFhmDZtmlFdEhGRrHQ68UF1+zYQFCQmhWQBLVlLeLiYlT0nBxg5Ejhxos4vYSP7PEj2ivMgEZFVLVkCJCSIv+4HDwbatZM7InJ0N28Cy5aJ5Udmz74zKamDsYt5kIiIqBJnzoh1sgDgoYfEX/dE1ubpCTz2mNhPShJL2tRhTJCIiGyJXg+MHQv88QcQEAA8/DDXW6Pa07kz0KQJUFYGPP20+Hmso/hbR0RkSz74ANizR9xa69ED4C18qk0KBfDUU6L+6OefxSjKOooJEhGRrThxApgxQ+y3awf8OfiEqFb5+gJxcWL/rbfq7DIkTJCIiGzBrVvAiBF3bq098ghvrZF8oqLEUiQ6HfC3vwF3LbVVV/C3j4jIFsycCRw5Ari7A/368dYayav8VpubG/Drr8CkSXJHVOuYIBERyW37duCf/xT7nTuL+WiI5ObpKaaYAIB//xvYskXWcGobEyQiIjlduACMHi32W7QA+vThhJBkO8LDgS5dxP7o0aI3qY5ggkREJJdbt4ChQ4ErV8SioY8+Km5pENmSAQNEXVxxsViS5NYtuSOqFUyQiIjk8tJLwKFDIinq1098CBHZGmdnMYDA1VUsRfL883JHVCuYIBERyeHf/wZWrRL7XbsCHTrIGw/RvSiVorcTADZuBBYtkjeeWsAEiYiotu3aBbz4othv2xbo3Zt1R2T7WrcWPZ2AGHW5fbus4VgbEyQiotp08qQYPl1WBgQHAwMHilsXRPagTx8xialeL5YiOXlS7oishgkSEVFtyc8XRa4aDeDnB/zlL0DDhnJHRVR95fMjBQaKou3+/QG1Wu6orIIJEhFRbdBogMcfB86fF0nRY48BKpXcURGZr149YORI8XOclyd6lQoL5Y7K4pggERFZW1GR6C3KzLwzU3arVnJHRVRzDRqIeZHc3YHTp8XSOMXFckdlUUyQiIisqaRE3JLYu1fUGvXpA3TqJHdURA/O1xeIjwdcXMSCtnFxDjVHEhMkIiJr+eMPMTR6xw7xIdKzJxAdzRFr5DhUKnG7zdlZ/BEQG+swPUlMkIiIrOHGDVFz9PXXomYjJgbo1Qtw4n+75GCaNQOeeUYkST/+KG633bwpd1QPjL+pRESW9vvvYtmQXbvu9Bz17cvkiBxX8+bAc8+JPwYOHBBze129KndUD4S/rURElvTrr0CPHuJDws1NJEZ9+jA5IsfXrBkwapT4oyA7G4iKAs6elTuqGuNvLBGRpezbJ2qMTp0CPDzErYYePZgcUd0REgL83/+JUW65uUCXLkBGhtxR1Qh/a4mILGHdOpEQXb0K+PiI+qOuXVmQTXWPvz8wfjzQqJGYH6lPH+CDDwBJkjsyszBBIiJ6EMXFwNixYk6YkhIgKAgYMkQsx8DkiOoqLy+RJIWFAbdvAxMnAs8+K0Z22gkmSERENXXiBNC9O7BmjUiGwsOBYcOAJk3kjoxIfq6uonC7Vy/x/YYNYg6wo0fljauamCAREZlLpwMWLQI6dxb/2devLz4EhgwRfzkTkaBQiPXannlGDFrIyRHF2wsWiN8jG8YEiYjIHCdPimRoxgxxS02lAp58Enj4YTF6h4gqatVK3GYLCQHKyoDERNH7asO9SUyQiIiqQ6MBXn4Z6NAB2L9f3D7o3Fn8ZdymDeuNiO6nYUNgzBixJEm9esBPPwGRkcCUKYBWK3d0FTBBIiK6l7IyYNUqkQS9/74oOA0MFL1Gjz8u/tMnoupRKETP0YsvinmT9Hpg6VKgRQtgxQqgtFTuCA0UkmRn4+5shFarhVKphEajgRdrDogcz+3bwCefAPPnA+fOiWNeXqIHqUcPUXdERA/mxAngm2/uLE3SpAnw1ltixJuzs1Vesrqf30yQaogJEpGDunlTzGmUnAycOSOOubuLGorevYHGjWUNj8jh6HTADz+IW9clJeJYaCgwcyYQHy9+/yyoup/f9Sz6qkRE9ionR9xK+/e/Rb0RIEbdtGwpbgkEB7POiMganJ2Bfv1Ez+yuXUBmJnD+PPDCC+J3ccYMWcJigkREddf168DmzaLH6MCBO8cbNhSLb3brJuqNmBgRWZ+rqyjg7tdP9CgdOyZmo5cJEyQiqlvOnwe+/FJsu3eLWiNAJEEBAeJWWufOgFLJxIhIDm5uQGys+H308JAtDCZIROTY8vOBPXuA9HSxnThh/Li3t5ibJSJC1D1wLiMi2yDzHyhMkIjIcfz+O5CdDWRlAYcPi3lWcnKM2ygUgJ+fmOCxTRtxK40j0ojIhE3Mg7RixQqEhobC3d0d0dHROHjw4D3bb9myBeHh4XB3d0dERAS2b99u9LgkSZg9ezYCAwNRv359xMbG4vTp00Ztrl+/jpEjR8LLywve3t4YO3YsbpYPMyQi26XVitmst20T8xJNmCC645s2BXx9gUceAaZPB9avv5MceXuLeVZ69hSLyo4bJ5YFeeghJkdEVCnZe5A2b96MhIQEpKSkIDo6GsnJyYiLi0NOTg78/f0rtN+3bx9GjBiBpKQk/OUvf8GGDRswePBgZGVloX379gCAhQsXYunSpVi3bh3CwsLwxhtvIC4uDidOnID7n8MFR44ciby8POzYsQNlZWUYM2YMxo8fjw0bNtTq9RPVaTodUFQken6uX6/49fp14PJlsV26JLb7/SHToIGoH/LxEUPyw8JELYObW+1cExE5BNnnQYqOjkbXrl2xfPlyAIBer0dISAgmT56MmTNnVmg/bNgwFBUVYdu2bYZj3bt3R2RkJFJSUiBJEoKCgvDyyy9j+vTpAACNRoOAgAB89NFHGD58OE6ePIl27drh0KFD6NKlCwAgNTUVgwYNwsWLFxEUFHTfuK02D9LevaJmwlRVb5M5xy1xDns/bkuxyHW8JufQ6UQxc1mZ+Hr3fmXHyvdLSoDi4sq3oqKaz5rr4iKKNz09xaZUittmgYFAo0Zi3hQWWBPZt2PHgFdeAaKjLXpau5gHqbS0FJmZmUhMTDQcc3JyQmxsLDIyMip9TkZGBhISEoyOxcXFYevWrQCAc+fOQa1WIzY21vC4UqlEdHQ0MjIyMHz4cGRkZMDb29uQHAFAbGwsnJyccODAATz11FMVXrekpAQl5RNYQSRdgPiHtqi5c4G0NMuek8jWKRSih8fFRazRVK+emBvF2Vnsu7qKpMfTUwzBb9BAtHcyqRL44w/g4kV5roGILOvWLfGHlIU/Z8s/t+/XPyRrgnT16lXodDoEBAQYHQ8ICMCpU6cqfY5ara60vVqtNjxefuxebUxv39WrVw++vr6GNqaSkpIwb968CsdDQkKqujwiqi5JEv8Z3roldyREZEu+/tpqp75x4waUSmWVj8teg2QvEhMTjXqu9Ho9rl+/jkaNGkFhwa58rVaLkJAQXLhwwWGXMHH0a+T12T9Hv0ZHvz7A8a+R11dzkiThxo0b9y2nkTVB8vPzg7OzM/JNam7y8/OhUqkqfY5Kpbpn+/Kv+fn5CAwMNGoTGRlpaFNQUGB0jtu3b+P69etVvq6bmxvcTIo8vb29732BD8DLy8shf+jv5ujXyOuzf45+jY5+fYDjXyOvr2bu1XNUTtZh/q6uroiKikLaXTU3er0eaWlpiImJqfQ5MTExRu0BYMeOHYb2YWFhUKlURm20Wi0OHDhgaBMTE4PCwkJkZmYa2nz//ffQ6/WItnAxGBEREdkf2W+xJSQkID4+Hl26dEG3bt2QnJyMoqIijBkzBgAwatQoBAcHIykpCQAwZcoU9O3bF++99x4ef/xxbNq0CT/99BM+/PBDAIBCocDUqVPx1ltvoVWrVoZh/kFBQRg8eDAAoG3bthgwYADGjRuHlJQUlJWVYdKkSRg+fHi1RrARERGRY5M9QRo2bBiuXLmC2bNnQ61WIzIyEqmpqYYi69zcXDjdNVKlR48e2LBhA2bNmoXXXnsNrVq1wtatWw1zIAHAjBkzUFRUhPHjx6OwsBC9evVCamqqYQ4kAFi/fj0mTZqE/v37w8nJCUOHDsXSpUtr78Kr4Obmhjlz5lS4nedIHP0aeX32z9Gv0dGvD3D8a+T1WZ/s8yARERER2RqbWGqEiIiIyJYwQSIiIiIywQSJiIiIyAQTJCIiIiITTJBsxPnz5zF27FiEhYWhfv36aNGiBebMmYNSk8U8jxw5gt69e8Pd3R0hISFYuHChTBHXzNtvv40ePXrAw8Ojyok2FQpFhW3Tpk21G2gNVef6cnNz8fjjj8PDwwP+/v545ZVXcPv27doN1IJCQ0MrvF8LFiyQO6waW7FiBUJDQ+Hu7o7o6GgcPHhQ7pAsZu7cuRXeq/DwcLnDqrE9e/bgr3/9K4KCgqBQKAxrcpaTJAmzZ89GYGAg6tevj9jYWJw+fVqeYGvoftc4evToCu/pgAED5AnWTElJSejatSsaNmwIf39/DB48GDk5OUZtbt26hYkTJ6JRo0bw9PTE0KFDK0wWbS1MkGzEqVOnoNfr8a9//QvHjx/HkiVLkJKSgtdee83QRqvV4rHHHkOzZs2QmZmJRYsWYe7cuYY5oOxBaWkpnn76aUyYMOGe7dauXYu8vDzDVj6Hla273/XpdDo8/vjjKC0txb59+7Bu3Tp89NFHmD17di1Halnz5883er8mT54sd0g1snnzZiQkJGDOnDnIyspCx44dERcXV2HmfXv20EMPGb1Xe/fulTukGisqKkLHjh2xYsWKSh9fuHAhli5dipSUFBw4cAANGjRAXFwcbtnRmn/3u0YAGDBggNF7unHjxlqMsOZ2796NiRMnYv/+/dixYwfKysrw2GOPoaioyNBm2rRp+Oqrr7Blyxbs3r0bly9fxpAhQ2onQIls1sKFC6WwsDDD9x988IHk4+MjlZSUGI69+uqrUps2beQI74GsXbtWUiqVlT4GQPr8889rNR5Lq+r6tm/fLjk5OUlqtdpwbOXKlZKXl5fR+2pPmjVrJi1ZskTuMCyiW7du0sSJEw3f63Q6KSgoSEpKSpIxKsuZM2eO1LFjR7nDsArT/zf0er2kUqmkRYsWGY4VFhZKbm5u0saNG2WI8MFV9n9jfHy89OSTT8oSj6UVFBRIAKTdu3dLkiTeLxcXF2nLli2GNidPnpQASBkZGVaPhz1INkyj0cDX19fwfUZGBvr06QNXV1fDsbi4OOTk5OD333+XI0SrmThxIvz8/NCtWzesWbMGkoNM15WRkYGIiAjDRKiAeA+1Wi2OHz8uY2QPZsGCBWjUqBE6deqERYsW2eUtw9LSUmRmZiI2NtZwzMnJCbGxscjIyJAxMss6ffo0goKC0Lx5c4wcORK5ublyh2QV586dg1qtNno/lUoloqOjHer9BID09HT4+/ujTZs2mDBhAq5duyZ3SDWi0WgAwPC5l5mZibKyMqP3MDw8HE2bNq2V91D2mbSpcmfOnMGyZcuwePFiwzG1Wo2wsDCjduUftGq1Gj4+PrUao7XMnz8fjzzyCDw8PPDdd9/hxRdfxM2bN/HSSy/JHdoDU6vVRskRYPwe2qOXXnoJnTt3hq+vL/bt24fExETk5eXh/ffflzs0s1y9ehU6na7S9+fUqVMyRWVZ0dHR+Oijj9CmTRvk5eVh3rx56N27N44dO4aGDRvKHZ5Flf8+VfZ+2uvvWmUGDBiAIUOGICwsDGfPnsVrr72GgQMHIiMjA87OznKHV216vR5Tp05Fz549DStjqNVquLq6VqjnrK33kD1IVjZz5sxKi47v3kz/87106RIGDBiAp59+GuPGjZMp8uqryTXeyxtvvIGePXuiU6dOePXVVzFjxgwsWrTIildwb5a+PntgzjUnJCSgX79+6NChA1544QW89957WLZsGUpKSmS+CjI1cOBAPP300+jQoQPi4uKwfft2FBYW4tNPP5U7NKqh4cOH44knnkBERAQGDx6Mbdu24dChQ0hPT5c7NLNMnDgRx44ds6kBOexBsrKXX34Zo0ePvmeb5s2bG/YvX76Mhx9+GD169KhQfK1SqSpU75d/r1KpLBNwDZh7jeaKjo7Gm2++iZKSElnW5bHk9alUqgqjomzhPTT1INccHR2N27dv4/z582jTpo0VorMOPz8/ODs7V/o7ZkvvjSV5e3ujdevWOHPmjNyhWFz5e5afn4/AwEDD8fz8fERGRsoUlfU1b94cfn5+OHPmDPr37y93ONUyadIkbNu2DXv27EGTJk0Mx1UqFUpLS1FYWGjUi1Rbv5NMkKyscePGaNy4cbXaXrp0CQ8//DCioqKwdu1ao0V6ASAmJgavv/46ysrK4OLiAgDYsWMH2rRpI+vtNXOusSays7Ph4+Mj26KFlry+mJgYvP322ygoKIC/vz8A8R56eXmhXbt2FnkNS3iQa87OzoaTk5Ph+uyFq6sroqKikJaWZhg1qdfrkZaWhkmTJskbnJXcvHkTZ8+exXPPPSd3KBYXFhYGlUqFtLQ0Q0Kk1Wpx4MCB+46itWcXL17EtWvXjJJCWyVJEiZPnozPP/8c6enpFUpIoqKi4OLigrS0NAwdOhQAkJOTg9zcXMTExNRKgGQDLl68KLVs2VLq37+/dPHiRSkvL8+wlSssLJQCAgKk5557Tjp27Ji0adMmycPDQ/rXv/4lY+Tm+e2336TDhw9L8+bNkzw9PaXDhw9Lhw8flm7cuCFJkiR9+eWX0qpVq6SjR49Kp0+flj744APJw8NDmj17tsyRV8/9ru/27dtS+/btpccee0zKzs6WUlNTpcaNG0uJiYkyR14z+/btk5YsWSJlZ2dLZ8+elT755BOpcePG0qhRo+QOrUY2bdokubm5SR999JF04sQJafz48ZK3t7fRqEN79vLLL0vp6enSuXPnpB9//FGKjY2V/Pz8pIKCArlDq5EbN24YfscASO+//750+PBh6bfffpMkSZIWLFggeXt7S1988YV05MgR6cknn5TCwsKkP/74Q+bIq+9e13jjxg1p+vTpUkZGhnTu3Dlp586dUufOnaVWrVpJt27dkjv0+5owYYKkVCql9PR0o8+84uJiQ5sXXnhBatq0qfT9999LP/30kxQTEyPFxMTUSnxMkGzE2rVrJQCVbnf7+eefpV69eklubm5ScHCwtGDBApkirpn4+PhKr3HXrl2SJEnSN998I0VGRkqenp5SgwYNpI4dO0opKSmSTqeTN/Bqut/1SZIknT9/Xho4cKBUv359yc/PT3r55ZelsrIy+YJ+AJmZmVJ0dLSkVCold3d3qW3bttI777xjF/85V2XZsmVS06ZNJVdXV6lbt27S/v375Q7JYoYNGyYFBgZKrq6uUnBwsDRs2DDpzJkzcodVY7t27ar09y0+Pl6SJDHU/4033pACAgIkNzc3qX///lJOTo68QZvpXtdYXFwsPfbYY1Ljxo0lFxcXqVmzZtK4cePsJqGv6jNv7dq1hjZ//PGH9OKLL0o+Pj6Sh4eH9NRTTxl1HFiT4s8giYiIiOhPHMVGREREZIIJEhEREZEJJkhEREREJpggEREREZlggkRERERkggkSERERkQkmSEREREQmmCARERERmWCCRER1nk6nQ48ePTBkyBCj4xqNBiEhIXj99ddlioyI5MKZtImIAPzyyy+IjIzEqlWrMHLkSADAqFGj8PPPP+PQoUNwdXWVOUIiqk1MkIiI/rR06VLMnTsXx48fx8GDB/H000/j0KFD6Nixo9yhEVEtY4JERPQnSZLwyCOPwNnZGUePHsXkyZMxa9YsucMiIhkwQSIiusupU6fQtm1bREREICsrC/Xq1ZM7JCKSAYu0iYjusmbNGnh4eODcuXO4ePGi3OEQkUzYg0RE9Kd9+/ahb9+++O677/DWW28BAHbu3AmFQiFzZERU29iDREQEoLi4GKNHj8aECRPw8MMPY/Xq1Th48CBSUlLkDo2IZMAeJCIiAFOmTMH27dvx888/w8PDAwDwr3/9C9OnT8fRo0cRGhoqb4BEVKuYIBFRnbd79270798f6enp6NWrl9FjcXFxuH37Nm+1EdUxTJCIiIiITLAGiYiIiMgEEyQiIiIiE0yQiIiIiEwwQSIiIiIywQSJiIiIyAQTJCIiIiITTJCIiIiITDBBIiIiIjLBBImIiIjIBBMkIiIiIhNMkIiIiIhMMEEiIiIiMvH/aYslbnaBSXwAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 生成正态分布的数据\n",
    "mean, std = 10, 4  # 均值和标准差\n",
    "x = np.linspace(-20, 20, 2000)\n",
    "y = np.exp(-(x - mean)**2 / (2 * std**2)) / (np.sqrt(2 * np.pi) * std)\n",
    "\n",
    "# 创建一个y轴的最小值，用于填充至该值\n",
    "y_min = np.min(y) * 0.1  # 可以根据需要调整这个值\n",
    "\n",
    "# 画图\n",
    "plt.plot(x, y, c='red', label='OUT')\n",
    "plt.ylim(0, 0.2)\n",
    "# 使用fill_between函数为曲线下面填色\n",
    "plt.fill_between(x, y_min, y, where=(y >= y_min), color='red', alpha=0.5)\n",
    "\n",
    "# plt.title('IN')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Probability Density')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "22a483f7-66aa-4920-b500-b6eabe336194",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e9cecf6a-1599-4b71-b844-dd24df804e4b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "opacus",
   "language": "python",
   "name": "opacus"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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